In a region of uniform electric field `vec(E) = E_(0) hat (i)` a semi cylinder is placed with it's rectangular shaped plane surface in y-z plane so that x-axis is normal to the plane surface. Given `l` is length and `r` is radius of cylinder the flux with curved surface alone is

Options

A. `E rl`
B. `(E rl)/(2)`
C. `2 E rl`
D. Zero

Answer

C

Explanation

`phi_(P)` = flux link with plane surface
`phi_(S)` = flux link with curved surface
since cylinder is not enclosing charge
`phi_(P) + phi_(S) =0`
`E (2 r l)+ phi_(S) = 0`
`phi_(S) = -2E rl`